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An approximate Taylor method for Stochastic Functional Differential Equations via polynomial condition Cover

An approximate Taylor method for Stochastic Functional Differential Equations via polynomial condition

Open Access
|Nov 2021

References

  1. [1] M. A. Atalla, Finite-difference approximations for stochastic differential equations, Probabilistic Methods for the Investigation of Systems with an Infinite number of Degrees of freedom, Inst. of Math. Acad. of Science USSR, Kiev, (1986) 11–16 (in Russian).
  2. [2] M. A. Atalla, On one approximating method for stochastic differential equations, Asymptotic Methods for the Theory of Stochastic processes, Inst. of Math. Acad. of Science USSR, Kiev, (1987) 15–21 (in Russian).
  3. [3] A. Bahar, X. Mao, Stochastic delay population dynamics, International J. Pure Appl. Math., 11 (2004) 377–400.
  4. [4] L. Collatz, “Functional analysis and numerical mathematics”, Academic Press, New York - San Francisco - London (1966).
  5. [5] T. M. Flett, “Differential analysis”, Cambridge University Press, Cambridge (1980).10.1017/CBO9780511897191
  6. [6] Y. Guo, W. Zhao, X. Ding, Input-to-state stability for stochastic multi-group models with multy-disperal and time-varying delay, App. Math. Comp., 343 (2019) 114–127.
  7. [7] D. J. Higham, X. Mao, A. M. Stuart, Strong convergence of Euler-type methods for nonlinear stochastic differential equations, SIAM J. Numer. Anal., 40 (3) (2002) 1041–1063.10.1137/S0036142901389530
  8. [8] M. Jansen, P. Pfaffelhuber, Stochastic gene expression with delay, J. Theor. Biol., 364 (2015) 355–363.
  9. [9] M. Jovanović, M. Krstić, The influence of time-dependent delay on behavior of stochastic population model with the Allee effect, App. Math. Modell., 39(2) (2015) 733–746.10.1016/j.apm.2014.06.019
  10. [10] V.B. Kolmanovskii, V.R. Nosov, Stability of Functional Differential Equations, Academic Press, 1986.
  11. [11] M. Krstić, The effect of stochastic perturbation on a nonlinear delay malaria epidemic model, Math. Comput. Simulat., 82(4) 558–569.10.1016/j.matcom.2011.09.003
  12. [12] M. Liu, C. Bai, Y. Jin, Population dynamical behavior of a two-predator one-prey stochastic model with time delay, Discrete Contin. Dyn. Sys. A, 37 (5) (2017) 2513–2538.10.3934/dcds.2017108
  13. [13] Q. Liu, D. Jiang, T. Hayat, A. Alsaedi, Dynamics of a stochastic SIR epidemic model with distributed delay and degenerate diffusion, J. Frankl. Inst., 356 (13) (2019) 7347–7370.10.1016/j.jfranklin.2019.06.030
  14. [14] X. Mao, “Stochastic differential equations and applications”, Horwood Publishing, Chichester, (2008).10.1533/9780857099402
  15. [15] X. Mao, S. Sabanis, Numerical solutions of stochastic differential delay equations under local Lipschitz condition, J. Comput. Appl. Math., 151 (2003) 215–227.
  16. [16] M. Milošević, M. Jovanović, S. Janković, An approximate method via Taylor series for stochastic functional differential equations, J. Math. Anal. Appl., 363 (2010) 128–137.
  17. [17] M. Obradović, M. Milošević, Stability of a class of neutral stochastic differential equations with unbounded delay and Markovian switching and the Euler?Maruyama method, J. Comput. Appl. Math., 244–266 (2017).10.1016/j.cam.2016.06.038
  18. [18] J. A. Oguntuase, On integral inequalities of Gronwall–Bellman–Bihari type in several variables, J. Ineq. Pure Appl. Math., 1 (2) (2000).
  19. [19] B. Øksendal, A. Sulem, T. Zhang, Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations, Adv. Appl. Probab., 43(2) (2011) 572–596.10.1239/aap/1308662493
  20. [20] M. Song, L. Hu, X. Mao, L. Zhang, Khasminskii-type theorems for stochastic functional differential equations, Discrete and continuous dynamical systems, series B, 18 (6) (2013) 1697–1714.10.3934/dcdsb.2013.18.1697
  21. [21] B. Tojtovska, S. Janković, General decay stability analysis of impulsive neural networks with mixed time delays, Neurocomputing, 142 (2014) 438–446.
  22. [22] M. Vasilova, Asymptotic behavior of a stochastic Gilpin–Ayala predator-prey system with time-dependent delay, Math. Comp. Model., 57 (3-4) (2013) 764–781.10.1016/j.mcm.2012.09.002
  23. [23] X. Wang, J. Yu, C. Li, H. Wang, T. Huang, J. Huang, Robust stability of stochastic fuzzy delayed neural networks with impulsive time window, Neural Networks, 67 (2015) 84–91.
  24. [24] F. Wu, X. Mao, Numerical solutions of neutral stochastic functional differential equations, SIAM J. Numer. Anal. 46 (2008) 1821–1841.10.1137/070697021
DOI: https://doi.org/10.2478/auom-2021-0037 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 105 - 133
Submitted on: Mar 22, 2021
Accepted on: Apr 30, 2021
Published on: Nov 23, 2021
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2021 Dušan D. Djordjević, Marija Milošević, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.